An Exploration of Vacuum-Decay Valleys

In the standard lore the decay of the false vacuum of a single-field potential is described by a semi-classical Euclidean bounce configuration that can be found using overshoot/undershoot algorithms, and whose action suppresses exponentially the decay rate. While this is generically correct, we show in a few concrete examples of potentials, previously studied in the literature for other purposes, that the vacuum decay structure can be far richer. In some cases there is no bounce and decay proceeds via the so-called pseudo-bounce configurations. In the general case with bounce, there are $2n+1$ bounces, with $n$ ranging from 0 (the standard case) to $\infty$. Some of these decay configurations we call antibounces as they have the wrong behavior for overshoot/undershoot algorithms, which can miss them. Bounce and antibounce configurations form $n$ pairs connected by pseudo-bounces. Our analysis benefits from a combined use of Euclidean and tunneling potential methods.